Transcendental Solutions of a Class of Minimal Functional Equations

Abstract

AbstractWe prove a result concerning power series f(z) 2 C[[z]] satisfying a functional equation of the form?where . In particular, we show that if f (z) satisfies a minimal functional equation of the above form with n≥ 2, then f (z) is necessarily transcendental. Towards a more complete classification, the case n = 1 is also considered.